Challenge

To forecast cryptocurrency prices using all the trading features like price, volume, open, high, low values present in the dataset.

Probably one of the biggest things in recent years is Bitcoin. Bitcoin grew by around 800% last year, held a market cap of around 250 billion dollars, and sparked worldwide interest in cryptocurrencies. But what are cryptocurrencies? Basically they’re digital currencies that use complex computer algorithms and encryption to generate more currency and to protect transactions. What’s really cool about cryptocurrencies is that they utilize a network of thousands of computers that forward people’s transactions to what’s known as a blockchain (essentially a big record of transactions kept secure by the network of computers). Once a transaction is in the blockchain, it’s never coming out again; this protects cryptocurrencies from double-spends. So it’s pretty clear that cryptocurrencies are a cool new way to spend money — what if we could predict how its prices fluctuate?

By analyzing bit coin historical features, such as bitcoin tradevolume, bitcoin blockssize, bitcoin difficultyto find a new block,total value of coinbase block rewards , transaction fees paid to miners, we can predict the variation and can predict the ups and downsof bitcoin price .

Data Description

Names Description
Date Date - Date of observation
btcmarketprice Numerical - Average USD market price across major bitcoin exchanges
btctotalbitcoins Numerical - Total number of bitcoins that have already been mined
btcmarketcap Numerical - Total USD value of bitcoin supply in circulation
btctradevolume Numerical - Total USD value of trading volume on major bitcoin exchanges
btcblockssize Numerical - Total size of all block headers and transactions
btcavgblock_size Numerical - Average block size in MB
btcnorphaned_blocks Numerical - Total number of blocks mined but ultimately not attached to blockchain
btcntransactionsperblock Numerical - Average number of transactions per block
btcmedianconfirmation_time Numerical - Median time for a transaction to be accepted into a mined block
btchashrate Numerical - Estimated number of tera hashes per second the Bitcoin network is performing
btc_difficulty Numerical - Relative measure of how difficult it is to find a new block
btcminersrevenue Numerical - Total value of coinbase block rewards and transaction fees paid to miners
btctransactionfees Numerical - Total value of all transaction fees paid to miners.
btccostpertransactionpercent Numerical - Miners revenue as percentage of the transaction volume.
btccostper_transaction Numerical - Miners revenue divided by the number of transactions
btcnunique_addresses Numerical - Total number of unique addresses used on the Bitcoin blockchain.
btcntransactions Numerical - Number of daily confirmed Bitcoin transactions
btcntransactions_total Numerical- Total number of transactions
btcntransactionsexcludingpopular Numerical- Total number of Bitcoin transactions, excluding the 100 most popular addresses
btcntransactionsexcludingchainslongerthan_100 Numerical- Total number of Bitcoin transactions per day excluding long transaction chains
btcoutputvolume Numerical- Total value of all transaction outputs per day
btcestimatedtransaction_volume Numerical- Total estimated value of transactions on the Bitcoin blockchain
btcestimatedtransactionvolumeusd Numerical- Estimated transaction value in USD value

Data Analysis

##                                               variable         mean
## 1                                     btc_market_price 1.156936e+03
## 2                                   btc_total_bitcoins 1.335988e+07
## 3                                       btc_market_cap 1.862023e+10
## 4                                     btc_trade_volume 1.056425e+08
## 5                                      btc_blocks_size 4.644976e+04
## 6                                   btc_avg_block_size 4.558738e-01
## 7                                btc_n_orphaned_blocks 4.596988e-01
## 8                         btc_n_transactions_per_block 8.670633e+02
## 9                         btc_median_confirmation_time 9.706814e+00
## 10                                       btc_hash_rate 1.793447e+06
## 11                                      btc_difficulty 2.335498e+11
## 12                                  btc_miners_revenue 2.953228e+06
## 13                                btc_transaction_fees 7.745935e+01
## 14                    btc_cost_per_transaction_percent 2.431859e+00
## 15                            btc_cost_per_transaction 1.812491e+01
## 16                              btc_n_unique_addresses 2.507467e+05
## 17                                  btc_n_transactions 1.317519e+05
## 18                            btc_n_transactions_total 9.027881e+07
## 19                btc_n_transactions_excluding_popular 1.218026e+05
## 20 btc_n_transactions_excluding_chains_longer_than_100 8.148942e+04
## 21                                   btc_output_volume 1.901380e+06
## 22                    btc_estimated_transaction_volume 2.322481e+05
## 23                btc_estimated_transaction_volume_usd 2.734628e+08
## 24                                                Days 1.770500e+03
##         std_dev variation_coef         p_01         p_05         p_25
## 1  2.674346e+03      2.3115755 4.154962e+00 5.159834e+00 1.078087e+02
## 2  2.576863e+06      0.1928807 7.950809e+06 8.632810e+06 1.130566e+07
## 3  4.497526e+10      2.4153979 3.305561e+07 4.602839e+07 1.219861e+09
## 4  3.496546e+08      3.3097915 1.248379e+05 2.511911e+05 3.828257e+06
## 5  4.566377e+04      0.9830788 6.181400e+02 8.577000e+02 8.477250e+03
## 6  3.454998e-01      0.7578847 1.646062e-02 2.382558e-02 1.452091e-01
## 7  9.225268e-01      2.0068068 0.000000e+00 0.000000e+00 0.000000e+00
## 8  6.730492e+02      0.7762400 3.600000e+01 5.100000e+01 3.042500e+02
## 9  3.280905e+00      0.3380002 5.633333e+00 6.266667e+00 7.487500e+00
## 10 3.746989e+06      2.0892672 8.496842e+00 1.075662e+01 1.458127e+02
## 11 4.764777e+11      2.0401546 1.155038e+06 1.498294e+06 1.933926e+07
## 12 6.460895e+06      2.1877402 2.852060e+04 3.945052e+04 4.705878e+05
## 13 1.288653e+02      1.6636505 3.490310e+00 6.457239e+00 1.457394e+01
## 14 1.901754e+00      0.7820164 4.825175e-01 6.451919e-01 1.044436e+00
## 15 2.357916e+01      1.3009257 1.056201e+00 1.820013e+00 5.846544e+00
## 16 2.080185e+05      0.8295965 9.457350e+03 1.230940e+04 5.769100e+04
## 17 1.011909e+05      0.7680411 5.598360e+03 7.162900e+03 5.163900e+04
## 18 8.654108e+07      0.9585979 2.084944e+06 2.681650e+06 1.962744e+07
## 19 1.039818e+05      0.8536909 4.074090e+03 5.375700e+03 2.626100e+04
## 20 6.993201e+04      0.8581729 5.219570e+03 6.405250e+03 2.473150e+04
## 21 2.438478e+06      1.2824783 3.185585e+05 4.395482e+05 8.253261e+05
## 22 2.376585e+05      1.0232961 5.774836e+04 8.201880e+04 1.492490e+05
## 23 6.587933e+08      2.4090782 4.552131e+05 7.998189e+05 1.893800e+07
## 24 6.519728e+02      0.3682422 6.645700e+02 7.548500e+02 1.206250e+03
##            p_50         p_75         p_95         p_99   skewness   kurtosis
## 1  3.814600e+02 6.772899e+02 6.113308e+03 1.513347e+04  4.0204186  20.208014
## 2  1.373259e+07 1.579800e+07 1.665550e+07 1.683308e+07 -0.4249548   2.022534
## 3  5.353668e+09 1.016825e+10 1.021500e+11 2.534300e+11  4.0331240  20.258732
## 4  1.619585e+07 4.004024e+07 5.424950e+08 1.795404e+09  6.5348233  60.776654
## 5  2.866300e+04 7.801137e+04 1.391994e+05 1.540718e+05  0.8882639   2.523000
## 6  3.532110e-01 7.937469e-01 1.014817e+00 1.063274e+00  0.3924264   1.627850
## 7  0.000000e+00 1.000000e+00 2.000000e+00 4.000000e+00  2.3975887   9.228294
## 8  6.255000e+02 1.467960e+03 2.076422e+03 2.290601e+03  0.5989092   2.008831
## 9  8.633333e+00 1.131667e+01 1.583583e+01 2.027150e+01  2.1363472  13.885025
## 10 3.068903e+05 1.571067e+06 9.968082e+06 1.986087e+07  3.2782429  14.839627
## 11 4.127287e+10 2.130000e+11 1.350000e+12 2.600000e+12  3.1601083  13.984572
## 12 1.243021e+06 2.249654e+06 1.308094e+07 4.025868e+07  4.6169422  26.617086
## 13 3.061101e+01 6.516377e+01 3.275609e+02 6.649762e+02  3.6877789  21.521243
## 14 1.743262e+00 3.270974e+00 6.298300e+00 9.093330e+00  1.6469959   6.094625
## 15 8.639663e+00 2.115561e+01 6.159131e+01 1.228364e+02  2.8345181  12.239496
## 16 1.969400e+05 4.082422e+05 6.064957e+05 8.683416e+05  0.7822109   2.967797
## 17 9.002350e+04 2.216978e+05 3.151295e+05 3.688130e+05  0.6628471   2.243549
## 18 5.701550e+07 1.472292e+08 2.672117e+08 2.961156e+08  0.9169656   2.596521
## 19 8.391800e+04 2.161795e+05 3.050850e+05 3.558842e+05  0.5973038   2.066496
## 20 4.881250e+04 1.391912e+05 2.108529e+05 2.463074e+05  0.7841609   2.341201
## 21 1.417049e+06 2.254076e+06 4.138097e+06 1.121818e+07  8.6344292 113.635350
## 22 2.090740e+05 2.765258e+05 4.059257e+05 5.508333e+05 15.1512301 298.006919
## 23 6.114545e+07 1.772323e+08 1.387115e+09 3.670032e+09  4.4027907  25.235036
## 24 1.770500e+03 2.334750e+03 2.786150e+03 2.876430e+03  0.0000000   1.800000
##             iqr                          range_98                      range_80
## 1  5.694811e+02        [4.1549616, 15133.4657326]       [7.836673, 2659.848803]
## 2  4.492341e+06               [7950809, 16833083]        [9458365, 16438351.25]
## 3  8.948388e+09       [33055607.5179, 2.5343e+11] [74040046.871, 43625054108.7]
## 4  3.621198e+07     [124837.85616, 1795404418.43]  [378879.64888, 176935221.49]
## 5  6.953412e+04           [618.14, 154071.771914]        [1821.7, 123564.74308]
## 6  6.485379e-01    [0.01646061914, 1.06327410774]  [0.0805532014, 0.9719768372]
## 7  1.000000e+00                            [0, 4]                        [0, 2]
## 8  1.163710e+03                [36, 2290.6014481]           [183, 1895.7315191]
## 9  3.829167e+00            [5.633333333, 20.2715]    [6.733333333, 14.01666667]
## 10 1.570921e+06 [8.49684165987, 19860869.4658999]   [13.90415045, 5539841.6282]
## 11 2.129807e+11            [1155038.334, 2.6e+12]       [1751454.535, 7.12e+11]
## 12 1.779066e+06    [28520.6011223, 40258679.6725]   [49403.55884, 5753362.8584]
## 13 5.058982e+01  [3.4903098398, 664.976218459999]  [10.905405781, 217.39422002]
## 14 2.226538e+00 [0.48251753199, 9.09332996994999]  [0.7489782871, 5.0801821246]
## 15 1.530906e+01    [1.05620133014, 122.836372308]  [2.7085213729, 44.071370197]
## 16 3.505512e+05              [9457.35, 868341.61]           [26482.8, 540912.9]
## 17 1.700588e+05                 [5598.36, 368813]           [27340.2, 282147.6]
## 18 1.276018e+08        [2084943.99, 296115558.68]      [4962182.2, 238282496.6]
## 19 1.899185e+05              [4074.09, 355884.24]           [10596.2, 275570.1]
## 20 1.144598e+05               [5219.57, 246307.4]             [11362.4, 191185]
## 21 1.428750e+06 [318558.514215, 11218178.2163999]   [528344.8656, 3231172.4742]
## 22 1.272768e+05             [57748.36, 550833.32]      [102573.2, 345053.54553]
## 23 1.582943e+08        [455213.09, 3670031860.53]       [1584638, 715790079.46]
## 24 1.128500e+03                 [664.57, 2876.43]               [867.7, 2673.3]

## 'data.frame':    2258 obs. of  11 variables:
##  $ btc_market_price                    : num  3.14 3.13 2.99 2.93 3.05 ...
##  $ btc_total_bitcoins                  : num  7787350 7794850 7801700 7809700 7817650 ...
##  $ btc_market_cap                      : num  24436704 24397803 23327083 22882421 23843832 ...
##  $ btc_trade_volume                    : num  181505 363126 263375 90500 170165 ...
##  $ btc_blocks_size                     : num  572 574 576 578 580 583 585 587 589 591 ...
##  $ btc_hash_rate                       : num  8.51 8.13 7.43 8.68 8.62 ...
##  $ btc_difficulty                      : num  1090716 1090716 1090716 1090716 1090716 ...
##  $ btc_miners_revenue                  : num  24646 23487 20490 23449 24257 ...
##  $ btc_transaction_fees                : num  4.3 4.09 3.51 3.62 3.5 ...
##  $ btc_cost_per_transaction            : num  3.9 4.24 3.87 3.69 3.45 ...
##  $ btc_estimated_transaction_volume_usd: num  10383421 11525011 9581607 5518235 17766452 ...

Prepare Data for Regression

## 'data.frame':    2258 obs. of  6 variables:
##  $ Market Price                    : num  3.14 3.13 2.99 2.93 3.05 ...
##  $ Market Cap                      : num  24436704 24397803 23327083 22882421 23843832 ...
##  $ Hash Rate                       : num  23 14 6 29 26 12 17 15 23 10 ...
##  $ Difficulty                      : num  1090716 1090716 1090716 1090716 1090716 ...
##  $ Miners Revenue                  : num  24646 23487 20490 23449 24257 ...
##  $ Estimated Transaction Volume USD: num  10383421 11525011 9581607 5518235 17766452 ...

Linear Regression To Predict Market Price

# setup cross validation and control parameters
metric <- "RMSE"
tuneLength <- 10

# Training process 
# Fit / train a Linear Regression model to  dataset
linearModelReg <- caret::train(btc_market_price~
                                 btc_market_cap+btc_hash_rate+
                                 btc_difficulty+btc_miners_revenue+
                                 btc_estimated_transaction_volume_usd
                       ,data=subTrain1, method="lm", metric=metric, 
                       preProc=c("center", "scale"), trControl=control, tuneLength = tuneLength)
## + Fold1.Rep1: intercept=TRUE 
## - Fold1.Rep1: intercept=TRUE 
## + Fold2.Rep1: intercept=TRUE 
## - Fold2.Rep1: intercept=TRUE 
## + Fold3.Rep1: intercept=TRUE 
## - Fold3.Rep1: intercept=TRUE 
## + Fold1.Rep2: intercept=TRUE 
## - Fold1.Rep2: intercept=TRUE 
## + Fold2.Rep2: intercept=TRUE 
## - Fold2.Rep2: intercept=TRUE 
## + Fold3.Rep2: intercept=TRUE 
## - Fold3.Rep2: intercept=TRUE 
## + Fold1.Rep3: intercept=TRUE 
## - Fold1.Rep3: intercept=TRUE 
## + Fold2.Rep3: intercept=TRUE 
## - Fold2.Rep3: intercept=TRUE 
## + Fold3.Rep3: intercept=TRUE 
## - Fold3.Rep3: intercept=TRUE 
## Aggregating results
## Fitting final model on full training set
summary(linearModelReg)
## 
## Call:
## lm(formula = .outcome ~ ., data = dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -462.15  -28.95  -10.49   14.14  204.46 
## 
## Coefficients:
##                                       Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)                          1138.6559     0.5804 1961.911  < 2e-16 ***
## btc_market_cap                       2422.4909     6.4585  375.086  < 2e-16 ***
## btc_hash_rate                        -126.0507     5.0542  -24.940  < 2e-16 ***
## btc_difficulty                        145.3881     5.7482   25.293  < 2e-16 ***
## btc_miners_revenue                    201.3575     4.9855   40.389  < 2e-16 ***
## btc_estimated_transaction_volume_usd   -9.2744     2.1326   -4.349 1.39e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 42.73 on 5415 degrees of freedom
## Multiple R-squared:  0.9997, Adjusted R-squared:  0.9997 
## F-statistic: 4.101e+06 on 5 and 5415 DF,  p-value: < 2.2e-16

Residual Analysis in Linear Regression

Linear Regression Prediction & Accuracy.

## [1] "RMSE 33.8595903089837"
## [1] "Error rate 0.0544967670074829"
## [1] "R2 0.999093423880329"

Polynominal Regression

poly_reg<-lm( btc_market_price~
                poly( btc_market_cap,2)+ poly( btc_hash_rate,2)+
             poly( btc_difficulty,2)+ poly( btc_miners_revenue,2)+
             poly( btc_estimated_transaction_volume_usd,2), data = subTrain1)
summary(poly_reg)
## 
## Call:
## lm(formula = btc_market_price ~ poly(btc_market_cap, 2) + poly(btc_hash_rate, 
##     2) + poly(btc_difficulty, 2) + poly(btc_miners_revenue, 2) + 
##     poly(btc_estimated_transaction_volume_usd, 2), data = subTrain1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -148.28  -11.54   -4.62   14.30  265.60 
## 
## Coefficients:
##                                                  Estimate Std. Error  t value
## (Intercept)                                     1.139e+03  3.568e-01 3191.369
## poly(btc_market_cap, 2)1                        1.795e+05  3.158e+02  568.435
## poly(btc_market_cap, 2)2                        1.135e+03  1.172e+02    9.681
## poly(btc_hash_rate, 2)1                        -1.127e+04  2.833e+02  -39.798
## poly(btc_hash_rate, 2)2                         8.981e+02  1.111e+02    8.080
## poly(btc_difficulty, 2)1                        9.082e+03  3.307e+02   27.467
## poly(btc_difficulty, 2)2                       -1.172e+03  1.142e+02  -10.258
## poly(btc_miners_revenue, 2)1                    1.788e+04  2.301e+02   77.726
## poly(btc_miners_revenue, 2)2                   -4.560e+03  8.601e+01  -53.019
## poly(btc_estimated_transaction_volume_usd, 2)1 -2.062e+03  1.208e+02  -17.063
## poly(btc_estimated_transaction_volume_usd, 2)2  5.619e+02  5.648e+01    9.950
##                                                Pr(>|t|)    
## (Intercept)                                     < 2e-16 ***
## poly(btc_market_cap, 2)1                        < 2e-16 ***
## poly(btc_market_cap, 2)2                        < 2e-16 ***
## poly(btc_hash_rate, 2)1                         < 2e-16 ***
## poly(btc_hash_rate, 2)2                        7.89e-16 ***
## poly(btc_difficulty, 2)1                        < 2e-16 ***
## poly(btc_difficulty, 2)2                        < 2e-16 ***
## poly(btc_miners_revenue, 2)1                    < 2e-16 ***
## poly(btc_miners_revenue, 2)2                    < 2e-16 ***
## poly(btc_estimated_transaction_volume_usd, 2)1  < 2e-16 ***
## poly(btc_estimated_transaction_volume_usd, 2)2  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26.27 on 5410 degrees of freedom
## Multiple R-squared:  0.9999, Adjusted R-squared:  0.9999 
## F-statistic: 5.426e+06 on 10 and 5410 DF,  p-value: < 2.2e-16

Polynomial Regression Prediction & Accuracy

## [1] "RMSE 33.8595903089837"
## [1] "Error rate 0.0544967670074829"
## [1] "R Square 0.999682461536609"

Spline Regression

knots <- quantile( subTrain1$btc_market_price, p = c( 0.25, 0.5, 0.75))

splinemodel<-lm( btc_market_price~
                bs( btc_market_cap, knots = knots)+ bs( btc_hash_rate, knots = knots)+
                bs( btc_difficulty, knots = knots)+ bs( btc_miners_revenue, knots = knots)+
                bs( btc_estimated_transaction_volume_usd, knots = knots), data = subTrain1)

Spline Regression Prediction & Accuracy

## [1] "RMSE 13.4968546288147"
## [1] "Error rate 0.0217230904251439"
## [1] "R Square 0.999810613324564"

Generalized Linear Model

lmfit6 <- gam(btc_market_price ~ btc_estimated_transaction_volume_usd + btc_miners_revenue, data=bitcoin_dataset)

summary(lmfit6)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## btc_market_price ~ btc_estimated_transaction_volume_usd + btc_miners_revenue
## 
## Parametric coefficients:
##                                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                          2.834e-11  4.107e-13    69.0   <2e-16 ***
## btc_estimated_transaction_volume_usd 8.448e-07  4.667e-08    18.1   <2e-16 ***
## btc_miners_revenue                   3.234e-04  4.686e-06    69.0   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Rank: 2/3
## R-sq.(adj) =  0.974   Deviance explained = 97.4%
## GCV = 1.8968e+05  Scale est. = 1.8951e+05  n = 2258

GAM Regression Prediction & Accuracy

## [1] "RMSE 241.540564283585"
## [1] "Error rate 0.388757800507882"
## [1] "R Square 0.958059200834039"

Scatter Plot 3D Visualization

## 
## Method: GCV   Optimizer: magic
## Model required no smoothing parameter selectionModel rank =  3 / 4

Penalized Cubic Regression Spline

mod_lm4 <- gam(btc_market_price ~ s(btc_total_bitcoins, bs="cr")+s(btc_avg_block_size, bs="cr")+
                 s(btc_transaction_fees, bs="cr"),
               data=bitcoin_dataset)
summary(mod_lm4)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## btc_market_price ~ s(btc_total_bitcoins, bs = "cr") + s(btc_avg_block_size, 
##     bs = "cr") + s(btc_transaction_fees, bs = "cr")
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1156.94      13.87    83.4   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                           edf Ref.df      F p-value    
## s(btc_total_bitcoins)   8.994  9.000 454.74  <2e-16 ***
## s(btc_avg_block_size)   8.120  8.686  13.66  <2e-16 ***
## s(btc_transaction_fees) 4.930  5.552 215.07  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.939   Deviance explained =   94%
## GCV = 4.3899e+05  Scale est. = 4.3451e+05  n = 2258

## 
## Method: GCV   Optimizer: magic
## Smoothing parameter selection converged after 17 iterations.
## The RMS GCV score gradient at convergence was 0.5643143 .
## The Hessian was positive definite.
## Model rank =  28 / 28 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                           k'  edf k-index p-value    
## s(btc_total_bitcoins)   9.00 8.99    0.14  <2e-16 ***
## s(btc_avg_block_size)   9.00 8.12    0.91  <2e-16 ***
## s(btc_transaction_fees) 9.00 4.93    1.00    0.45    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Cubic Regression Spline Prediction & Accuracy

## [1] "RMSE 164.983422387511"
## [1] "Error rate 0.265539631398429"
## [1] "R Square 0.979740412173328"

Extreme Gradient Boosting

xgbGrid <- expand.grid(nrounds = c(140,160),  # this is n_estimators in the python code above
                       max_depth = c(10, 15, 20, 25),
                       colsample_bytree = seq(0.5, 0.9, length.out = 5),
                       ## The values below are default values in the sklearn-api. 
                       eta = 0.3,
                       gamma=0,
                       min_child_weight = 1,
                       subsample = 1
)

model_xgb <- train(btc_market_price ~ .,
                   data = subTrain,
                   method = "xgbTree",
                   preProcess = c("scale", "center"),
                   trControl = trainControl(method = "repeatedcv", 
                                            number = 5, 
                                            repeats = 3, 
                                            verboseIter = FALSE),
                   tuneGrid = xgbGrid,
                   verbose = 0)
## [18:58:31] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
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## [19:02:15] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:17] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:18] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:20] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:21] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:23] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:24] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:25] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:26] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:27] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:29] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:30] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:31] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:32] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:33] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:34] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:36] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:37] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:38] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:40] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:41] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:43] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:44] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:45] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:46] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:48] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:49] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:50] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:51] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:52] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:54] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:55] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:56] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:57] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:02:58] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:00] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:02] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:03] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:04] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:06] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:08] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:10] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:12] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:13] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:14] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:16] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:17] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:18] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:19] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:21] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:22] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:23] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:24] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:25] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:27] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:28] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:29] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:31] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:32] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:34] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:36] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:38] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:39] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:40] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:41] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:42] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:44] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:45] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:46] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:47] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:49] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:50] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:51] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:52] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:53] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:54] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:55] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:57] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:03:58] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:00] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:02] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:03] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:04] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:06] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:07] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:08] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:10] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:11] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:13] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:15] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:16] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:18] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:18] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:20] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:21] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:22] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:24] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:25] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:27] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:28] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:30] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:32] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:33] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:34] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:36] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:37] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:38] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:39] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:41] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:42] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:43] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:44] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:45] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:46] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:48] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:49] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:50] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:51] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:53] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:55] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:57] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:04:58] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:00] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:01] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:02] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:03] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:05] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:06] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:07] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:08] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:10] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
## [19:05:11] WARNING: amalgamation/../src/objective/regression_obj.cu:174: reg:linear is now deprecated in favor of reg:squarederror.
model_xgb$results   
##    eta max_depth gamma colsample_bytree min_child_weight subsample nrounds
## 1  0.3        10     0              0.5                1         1     140
## 3  0.3        10     0              0.6                1         1     140
## 5  0.3        10     0              0.7                1         1     140
## 7  0.3        10     0              0.8                1         1     140
## 9  0.3        10     0              0.9                1         1     140
## 11 0.3        15     0              0.5                1         1     140
## 13 0.3        15     0              0.6                1         1     140
## 15 0.3        15     0              0.7                1         1     140
## 17 0.3        15     0              0.8                1         1     140
## 19 0.3        15     0              0.9                1         1     140
## 21 0.3        20     0              0.5                1         1     140
## 23 0.3        20     0              0.6                1         1     140
## 25 0.3        20     0              0.7                1         1     140
## 27 0.3        20     0              0.8                1         1     140
## 29 0.3        20     0              0.9                1         1     140
## 31 0.3        25     0              0.5                1         1     140
## 33 0.3        25     0              0.6                1         1     140
## 35 0.3        25     0              0.7                1         1     140
## 37 0.3        25     0              0.8                1         1     140
## 39 0.3        25     0              0.9                1         1     140
## 2  0.3        10     0              0.5                1         1     160
## 4  0.3        10     0              0.6                1         1     160
## 6  0.3        10     0              0.7                1         1     160
## 8  0.3        10     0              0.8                1         1     160
## 10 0.3        10     0              0.9                1         1     160
## 12 0.3        15     0              0.5                1         1     160
## 14 0.3        15     0              0.6                1         1     160
## 16 0.3        15     0              0.7                1         1     160
## 18 0.3        15     0              0.8                1         1     160
## 20 0.3        15     0              0.9                1         1     160
## 22 0.3        20     0              0.5                1         1     160
## 24 0.3        20     0              0.6                1         1     160
## 26 0.3        20     0              0.7                1         1     160
## 28 0.3        20     0              0.8                1         1     160
## 30 0.3        20     0              0.9                1         1     160
## 32 0.3        25     0              0.5                1         1     160
## 34 0.3        25     0              0.6                1         1     160
## 36 0.3        25     0              0.7                1         1     160
## 38 0.3        25     0              0.8                1         1     160
## 40 0.3        25     0              0.9                1         1     160
##        RMSE  Rsquared      MAE    RMSESD   RsquaredSD     MAESD
## 1  39.03400 0.9997143 3.867351 25.023371 3.546794e-04 1.7577150
## 3  33.18108 0.9998120 3.425709 17.872421 1.829663e-04 1.3737375
## 5  37.31503 0.9997661 3.674326 19.179381 2.239330e-04 1.5042837
## 7  22.10033 0.9999162 2.489683 10.446471 8.835360e-05 0.9782250
## 9  19.15121 0.9999365 2.228535  9.277475 6.452859e-05 0.7787798
## 11 44.45382 0.9996732 4.240647 22.769227 3.019777e-04 1.5515580
## 13 29.11588 0.9998498 3.121364 16.054773 1.656704e-04 1.3285063
## 15 27.35755 0.9998652 2.875670 16.348729 1.340044e-04 1.4208245
## 17 20.72887 0.9999220 2.417198 12.214128 9.424477e-05 1.1041989
## 19 17.78226 0.9999508 2.127081  6.524760 3.807719e-05 0.6610867
## 21 42.59284 0.9996913 3.991861 22.418154 2.996915e-04 1.3100600
## 23 31.25821 0.9998335 3.172345 15.587641 1.466992e-04 1.2304602
## 25 28.70454 0.9998739 2.949386 10.537141 9.008602e-05 0.7973135
## 27 23.29094 0.9999056 2.660002 12.429602 9.178515e-05 1.1248811
## 29 19.26550 0.9999407 2.247684  7.132943 4.805357e-05 0.7821813
## 31 36.03812 0.9998017 3.798457 13.336798 1.265363e-04 0.9967262
## 33 27.92913 0.9998598 3.068617 15.623109 1.469525e-04 1.6367994
## 35 24.71652 0.9998876 2.767246 14.545188 1.309887e-04 1.2894564
## 37 20.78230 0.9999266 2.390776  9.009320 6.746089e-05 0.8252055
## 39 20.65820 0.9999333 2.252980  7.886065 5.210519e-05 0.7411809
## 2  39.03396 0.9997143 3.840191 25.023252 3.546726e-04 1.7560321
## 4  33.18124 0.9998120 3.401858 17.872200 1.829661e-04 1.3735135
## 6  37.31472 0.9997661 3.652922 19.179483 2.239312e-04 1.5032044
## 8  22.10016 0.9999162 2.469937 10.446723 8.835524e-05 0.9790382
## 10 19.15092 0.9999365 2.211328  9.277738 6.453012e-05 0.7808012
## 12 44.45381 0.9996732 4.240394 22.769204 3.019772e-04 1.5515495
## 14 29.11586 0.9998498 3.121129 16.054796 1.656708e-04 1.3285211
## 16 27.35753 0.9998652 2.875456 16.348726 1.340042e-04 1.4208145
## 18 20.72887 0.9999220 2.417110 12.214123 9.424471e-05 1.1041939
## 20 17.78226 0.9999508 2.126974  6.524756 3.807719e-05 0.6611015
## 22 42.59281 0.9996913 3.991856 22.418093 2.996899e-04 1.3100574
## 24 31.25817 0.9998335 3.172340 15.587609 1.466987e-04 1.2304575
## 26 28.70448 0.9998739 2.949379 10.537133 9.008597e-05 0.7973170
## 28 23.29092 0.9999056 2.659998 12.429597 9.178509e-05 1.1248812
## 30 19.26545 0.9999407 2.247677  7.132948 4.805362e-05 0.7821824
## 32 36.03809 0.9998017 3.798454 13.336753 1.265357e-04 0.9967265
## 34 27.92913 0.9998598 3.068615 15.623119 1.469526e-04 1.6368023
## 36 24.71647 0.9998876 2.767241 14.545150 1.309883e-04 1.2894575
## 38 20.78225 0.9999266 2.390771  9.009340 6.746094e-05 0.8252071
## 40 20.65812 0.9999333 2.252975  7.886036 5.210475e-05 0.7411819
plot(model_xgb)

Extreme Gradient Boosting Prediction & Accuracy

## MSE:  80.92633 MAE:  5.168907  RMSE:  8.995907

## [1] "RMSE 8.99590656624651"
## [1] "Error rate 0.0133612673135272"
## [1] "R Square 0.999954333588047"

Compare Regression Models

## 'data.frame':    1 obs. of  4 variables:
##  $ Algorithm: chr "Linear Regression"
##  $ RMSE     : num 33.9
##  $ R2       : num 0.999
##  $ Error    : num 0.0545
## 'data.frame':    1 obs. of  4 variables:
##  $ Algorithm: chr "Polynomial Regression"
##  $ RMSE     : num 33.9
##  $ R2       : num 1
##  $ Error    : num 0.0545
## 'data.frame':    1 obs. of  4 variables:
##  $ Algorithm: chr "Spline Regression"
##  $ RMSE     : num 13.5
##  $ R2       : num 1
##  $ Error    : num 0.0217
## 'data.frame':    1 obs. of  4 variables:
##  $ Algorithm: chr "GAM Regression"
##  $ RMSE     : num 242
##  $ R2       : num 0.958
##  $ Error    : num 0.389
## 'data.frame':    1 obs. of  4 variables:
##  $ Algorithm: chr "Cubic Regression Spline"
##  $ RMSE     : num 165
##  $ R2       : num 0.98
##  $ Error    : num 0.266
## 'data.frame':    1 obs. of  4 variables:
##  $ Algorithm: chr "Extreme Gradient Boosting"
##  $ RMSE     : num 9
##  $ R2       : num 1
##  $ Error    : num 0.0134

Conclusion

As such, we provide evidence suggesting that technical analysis is useful in a market like bitcoin whose value is mainly driven by by fundamental factors. Extreme Gradient Boosting outperforms other model with lesser error and with R2=1 the model completely fit.